With the Moon as our starting point to link the Ways of Knowing (WOK's - Think PERL) and the Areas of Knowing (AOK's - Think IB Hexogram - Math / Natural Sciences / Human Sciences / Arts / History) we will a) make sense of some of the Math questions raised in our Moon Perception exercise and b) have fun interpreting some quotations about Math as an AOK.
Copy the following onto your Math page and add your thinking:
A. Record here 3 Math Questions raised in class that interest you. Then under each write your answer/s and reflect on your process for expanding your knowledge in that area.
Q1. How many moons would fit inside the earth?
49 moons would fit inside the earth.
Q2. How much is the surface area of the moon? The surface area of the moon is 14,658,000 square miles or 9.4 billion acres.
Q3. What is the size of the moon compared to the earth? The moon is about 1/4 the size of the Earth.
Q1. What is the velocity of the Moon's Orbit?
roughly 1km/s
Q2. What is the average distance of the moon from the Earth? Average Center to Center distance is 384.403 km
Q3. How many moons can you fit into the earth? Just using their volumes and not taking shape into consideration, roughly 49 moons can be put into Earth
Q3. What is the diameter of the largest crater on the moon that can be from Earth with the naked eye? It cannot be seen with the naked eye.
Q2. How much light does the moon produce? None, it reflects light form the sun it does not produce light.
How many craters are there in the moon? "Impact craters are the remains of collisions between an asteroid, comet, or meteorite and the Moon."http://www.enchantedlearning.com/subjects/astronomy/moon/Craters.shtml. There are said to be indefinite amount of craters on the Moon and that it is impossible to count how many there are, because if we keep looking closer and closer at the Moon we will notice even more craters, even craters that are invisible to the naked eye! Also every now and again there are objects in space hitting the Moon causing more craters, and therefore leaves us with no definite answer!
Question 2. How many craters are there in the moon In the moon, there are holes caused by the meteors that hit the surface of the moon due to the lack of the air hemisphere. On the moons' surface, the craters that have a diameter more than 1 km are approximately 300,000. Other craters that are smaller cannot really be counted, they are millions. The count for the 300 craters was approximated, by the scopes from the earth and by the satellites.
What is the size of our moon compared to other moons? There are four other moons that are larger than our Moon in our solar system. They are Ganymede, which orbits around Jupiter, Titan, Callisto and Io. The moons named Callisto and Io orbit around Jupiter, while the moon Titan orbits around the planet Saturn. There is one moon that is known by the name of Europa, which is a moon of Jupiter. This last moon is one of the four largest moons in our solar system including those moons mentioned previously, yet Europa is known to be smaller than our Moon.
*What is the Escape Velocity of the moon?
2.38 km/s
B. Read the following Math quotations (some you may have heard before) and below three of them, write your interpretation of what you believe the author is trying to say.
"Mathematics is neither physical nor mental, it's social." Reuben Hersh, 1927-
The author is saying that mathematics is social. I don't agree with him, how can mathematics be social? I personally see that math is a physical and mental process.
"The useful combinations (in mathematics) are precisely the most beautiful." Henri Poincare, 1854-1912
The author is saying that the most interesting thing in mathematics is the different ways you can use math in life. "Mathematics is the abstract key with turns the lock of the physical universe." John Polkinghorne, 1930 -
"Everything that can be counted does not count. Everything that counts cannot be counted." Albert Einstein, 1879-1955
I conclude from the two sentences that eventually nothing can be counted. But I am not sure what the scientist is trying to say.
"The mark of a civilized man is the ability to look at a column of numbers and weep." Berterand Russell, 1872-1970
"A mathematician is a machine for turning coffee into theorems." Paul Erdos, 1913-96
"Mathematics began when it was discovered that a barce of pheasants, and a couple of days have something in common: the number two." Bertrand Russell, 1872-1970
To speak freely, I am convinced that it (mathematics) is a more powerful instrument of knowledge than any other..." Rene Descaret, 1596-1650
"Instead of having "answers" on a math test, they should just call them 'impressions", and if you got a different "impression", so what, cant' we all be brothers?| Jack Handy 1949-
Math helps us understand the world - Essay
Albert Einstein once said “Pure mathematics is, in its way, the poetry of logical ideas.” We see many people in our lives that hate mathematics and struggle with it. Almost all of them think that math is a complicated and a hard subject, and it doesn’t help us in our daily lives. I would say that math helps us in so many aspects in order to understand the world better. Mathematics is a logical process. So the more we know about math the better we will become at understanding all things because it teaches us to reason and think logically. It’s also an important valuable subject that has a lot of benefits, especially that we’re living at the 21st century where knowledge and experience are very significant requirements to achieve a better future. Most of university majors need math like all kinds of natural sciences subjects, engineering, economics, finance, and even philosophy. Therefore knowing math will give us a better opportunity for our futures. We use simple mathematics in our daily live. For example if we went to a market to buy food then we use math in counting money. Another example would be if we were at the street and someone asked us about the directions of a certain place then we use math to explain to him by meters or kilometers or even by blocks, we use numbers in all of them. And there are a lot of uses of math like how to handle money, telling time, cooking, sharing things, or knowing how many of any item will be left if some are used. All that makes our lives easier. In conclusion math helps us understand the world and it improves our radical thinking skills and grab the true meaning of a lot of things.
Option I
Dear (someone), My school asked us to do a research about a mathematician. It was hard to choose just one mathematician among the others. They were all great thinkers. Theory of knowledge encourages critical thinking about knowledge itself, to try to help young people make sense of what they encounter. The fact that a lot of people struggle with math and hates it, TOK tries to help them understand it in a better way and think of it as an area of knowledge. In math we use deductive reasoning, which is the process of using rules to arrive at a specific conclusion drawn from general statements. And we also use theorems which are statements proved on the basis of previously accepted or established statements and principles. Abu Ja’far Muhammad ibn Musa Al-Khwarizmi was an Islamic mathematician who wrote on Hindu-Arabic numerals and was among the first to use zero as a place holder in positional notation. He was born in Baghdad in 780 and one of the learned men who worked in the House of Wisdom the first famous library established after the library of Alexandria was destroyed and it included translated scientific work. His interests lied in the fields of algebra, geometry, astronomy and geography. His most famous work is Hisab al-jabr w'al-muqabala, which we got the name algebra from. He influenced lots of people in all parts of the world. Al-Khwarizmi was a notable mathematician along with an abundance of other attributes. After reading Al-Khwarizmi’s biography and doing some research in math there are some questions that were raised in my mind. Like what counts as understanding in math? Is it sufficient to get the right answer to a problem and then say that one understands the concept and it relevance to the world. And are there aspects of math that one can choose whether or not to believe? Sources: http://www.ms.uky.edu/~carl/ma330/project2/al-khwa21.html http://en.wikipedia.org/wiki/Muḥammad_ibn_Mūsā_al-Khwārizmī http://www-history.mcs.st-and.ac.uk/Mathematicians/Al-Khwarizmi.html Thank you, Alhanouf
How have technological innovations, such as developments in computing, affected the nature and practice of mathematics? MIRAL, HANOUF, DANA, RAZAN Technology has affected the nature and practice of mathematics in such a way that it disables us to have the ability to do any sort of mental math, develop our radical thinking and exercise our brains. Developments such as calculators, computers and the applications used, do all the thinking for us where we just sit around, type what we want and wait for an answer. It has affected the practice of mathematics as we are not able to understand fully the methods and techniques used because we are all dependent on a calculator to do everything for us. It can be seen that students nowadays are more dependent on the calculator to do the calculations for them, instead of them broadening their abilities and developing their understanding.
Technology also doesn't affect the nature and practice of mathematics in some ways, some would argue, because when we apply complex methods and formulas, we need to know most by heart and learn when to apply them and how. This part of math, technology cannot help us with, although it is used to obtain a final answer, but it's not used in the process of writing and solving the formula or equation. An example would be trying to see which formula, Un = U1 r^n-1 or Un = n/2 (U1 + (n-1) d) to use, to find the amount of terms in a sequence. You would have to use a calculator eventually to obtain the final answer, but technology would not be able to interfere with applying the method, rearranging the formula and simplifying it down. This all has to be done mentally.
It depends which way you look at it. There is always two sides to a story, and usually one case would seem more reasonable than the other, although in this case it seems that both cases can work out perfectly, if applied to the correct situation.
Math as an Area of Knowing
With the Moon as our starting point to link the Ways of Knowing (WOK's - Think PERL) and the Areas of Knowing (AOK's - Think IB Hexogram - Math / Natural Sciences / Human Sciences / Arts / History) we will a) make sense of some of the Math questions raised in our Moon Perception exercise and b) have fun interpreting some quotations about Math as an AOK.
Copy the following onto your Math page and add your thinking:
A. Record here 3 Math Questions raised in class that interest you. Then under each write your answer/s and reflect on your process for expanding your knowledge in that area.
Q1. How many moons would fit inside the earth?
49 moons would fit inside the earth.
Q2. How much is the surface area of the moon?
The surface area of the moon is 14,658,000 square miles or 9.4 billion acres.
Q3. What is the size of the moon compared to the earth?
The moon is about 1/4 the size of the Earth.
Q1. What is the velocity of the Moon's Orbit?
roughly 1km/s
Q2. What is the average distance of the moon from the Earth?
Average Center to Center distance is 384.403 km
Q3. How many moons can you fit into the earth?
Just using their volumes and not taking shape into consideration, roughly 49 moons can be put into Earth
Q3. What is the diameter of the largest crater on the moon that can be from Earth with the naked eye?
It cannot be seen with the naked eye.
Q2. How much light does the moon produce?
None, it reflects light form the sun it does not produce light.
How many craters are there in the moon?
"Impact craters are the remains of collisions between an asteroid, comet, or meteorite and the Moon."http://www.enchantedlearning.com/subjects/astronomy/moon/Craters.shtml. There are said to be indefinite amount of craters on the Moon and that it is impossible to count how many there are, because if we keep looking closer and closer at the Moon we will notice even more craters, even craters that are invisible to the naked eye! Also every now and again there are objects in space hitting the Moon causing more craters, and therefore leaves us with no definite answer!
Question 2. How many craters are there in the moon
In the moon, there are holes caused by the meteors that hit the surface of the moon due to the lack of the air hemisphere. On the moons' surface, the craters that have a diameter more than 1 km are approximately 300,000. Other craters that are smaller cannot really be counted, they are millions. The count for the 300 craters was approximated, by the scopes from the earth and by the satellites.
What is the size of our moon compared to other moons?
There are four other moons that are larger than our Moon in our solar system. They are Ganymede, which orbits around Jupiter, Titan, Callisto and Io. The moons named Callisto and Io orbit around Jupiter, while the moon Titan orbits around the planet Saturn. There is one moon that is known by the name of Europa, which is a moon of Jupiter. This last moon is one of the four largest moons in our solar system including those moons mentioned previously, yet Europa is known to be smaller than our Moon.
*What is the Escape Velocity of the moon?
2.38 km/s
B. Read the following Math quotations (some you may have heard before) and below three of them, write your interpretation of what you believe the author is trying to say.
"Mathematics is neither physical nor mental, it's social." Reuben Hersh, 1927-
The author is saying that mathematics is social. I don't agree with him, how can mathematics be social? I personally see that math is a physical and mental process.
"The useful combinations (in mathematics) are precisely the most beautiful." Henri Poincare, 1854-1912
The author is saying that the most interesting thing in mathematics is the different ways you can use math in life.
"Mathematics is the abstract key with turns the lock of the physical universe." John Polkinghorne, 1930 -
"Everything that can be counted does not count. Everything that counts cannot be counted." Albert Einstein, 1879-1955
I conclude from the two sentences that eventually nothing can be counted. But I am not sure what the scientist is trying to say.
"The mark of a civilized man is the ability to look at a column of numbers and weep." Berterand Russell, 1872-1970
"A mathematician is a machine for turning coffee into theorems." Paul Erdos, 1913-96
"Mathematics began when it was discovered that a barce of pheasants, and a couple of days have something in common: the number two." Bertrand Russell, 1872-1970
To speak freely, I am convinced that it (mathematics) is a more powerful instrument of knowledge than any other..." Rene Descaret, 1596-1650
"Instead of having "answers" on a math test, they should just call them 'impressions", and if you got a different "impression", so what, cant' we all be brothers?| Jack Handy 1949-
Math helps us understand the world - Essay
Albert Einstein once said “Pure mathematics is, in its way, the poetry of logical ideas.” We see many people in our lives that hate mathematics and struggle with it. Almost all of them think that math is a complicated and a hard subject, and it doesn’t help us in our daily lives. I would say that math helps us in so many aspects in order to understand the world better. Mathematics is a logical process. So the more we know about math the better we will become at understanding all things because it teaches us to reason and think logically. It’s also an important valuable subject that has a lot of benefits, especially that we’re living at the 21st century where knowledge and experience are very significant requirements to achieve a better future. Most of university majors need math like all kinds of natural sciences subjects, engineering, economics, finance, and even philosophy. Therefore knowing math will give us a better opportunity for our futures. We use simple mathematics in our daily live. For example if we went to a market to buy food then we use math in counting money. Another example would be if we were at the street and someone asked us about the directions of a certain place then we use math to explain to him by meters or kilometers or even by blocks, we use numbers in all of them. And there are a lot of uses of math like how to handle money, telling time, cooking, sharing things, or knowing how many of any item will be left if some are used. All that makes our lives easier. In conclusion math helps us understand the world and it improves our radical thinking skills and grab the true meaning of a lot of things.
Option I
Dear (someone),My school asked us to do a research about a mathematician. It was hard to choose just one mathematician among the others. They were all great thinkers. Theory of knowledge encourages critical thinking about knowledge itself, to try to help young people make sense of what they encounter. The fact that a lot of people struggle with math and hates it, TOK tries to help them understand it in a better way and think of it as an area of knowledge. In math we use deductive reasoning, which is the process of using rules to arrive at a specific conclusion drawn from general statements. And we also use theorems which are statements proved on the basis of previously accepted or established statements and principles. Abu Ja’far Muhammad ibn Musa Al-Khwarizmi was an Islamic mathematician who wrote on Hindu-Arabic numerals and was among the first to use zero as a place holder in positional notation. He was born in Baghdad in 780 and one of the learned men who worked in the House of Wisdom the first famous library established after the library of Alexandria was destroyed and it included translated scientific work. His interests lied in the fields of algebra, geometry, astronomy and geography. His most famous work is Hisab al-jabr w'al-muqabala, which we got the name algebra from. He influenced lots of people in all parts of the world. Al-Khwarizmi was a notable mathematician along with an abundance of other attributes. After reading Al-Khwarizmi’s biography and doing some research in math there are some questions that were raised in my mind. Like what counts as understanding in math? Is it sufficient to get the right answer to a problem and then say that one understands the concept and it relevance to the world. And are there aspects of math that one can choose whether or not to believe?
Sources:
http://www.ms.uky.edu/~carl/ma330/project2/al-khwa21.html
http://en.wikipedia.org/wiki/Muḥammad_ibn_Mūsā_al-Khwārizmī
http://www-history.mcs.st-and.ac.uk/Mathematicians/Al-Khwarizmi.html
Thank you,
Alhanouf
How have technological innovations, such as developments in computing, affected the nature and practice of mathematics? MIRAL, HANOUF, DANA, RAZAN
Technology has affected the nature and practice of mathematics in such a way that it disables us to have the ability to do any sort of mental math, develop our radical thinking and exercise our brains. Developments such as calculators, computers and the applications used, do all the thinking for us where we just sit around, type what we want and wait for an answer. It has affected the practice of mathematics as we are not able to understand fully the methods and techniques used because we are all dependent on a calculator to do everything for us. It can be seen that students nowadays are more dependent on the calculator to do the calculations for them, instead of them broadening their abilities and developing their understanding.
Technology also doesn't affect the nature and practice of mathematics in some ways, some would argue, because when we apply complex methods and formulas, we need to know most by heart and learn when to apply them and how. This part of math, technology cannot help us with, although it is used to obtain a final answer, but it's not used in the process of writing and solving the formula or equation. An example would be trying to see which formula, Un = U1 r^n-1 or Un = n/2 (U1 + (n-1) d) to use, to find the amount of terms in a sequence. You would have to use a calculator eventually to obtain the final answer, but technology would not be able to interfere with applying the method, rearranging the formula and simplifying it down. This all has to be done mentally.
It depends which way you look at it. There is always two sides to a story, and usually one case would seem more reasonable than the other, although in this case it seems that both cases can work out perfectly, if applied to the correct situation.